Not applicable.
This invention relates generally to profilometry and more particularly, to image deconvolution techniques for probe scanning devices.
As is known in the art, a structure having one characteristic dimension (e.g. height) which is more pronounced than the others (e.g. width and length) is referred to as a high aspect ratio structure. Examples of these type of structures include probes of atomic force and scanning tunnelling microscopes, field emission probes, micro-indenters and Micro Electro-Mechanical systems (MEM""s) structures. Other high aspect ratio structures are found in quantum magnetic media for high-density data storage, compact disk stampers, crystalline structures, blades and biological systems such as virus particles. Such high aspect ratio structures have typical heights on the order of tens of micrometers and tip radii in the range of tens of nanometers. Further, these structures may or may not be conductive.
Obtaining images of high aspect ratio structures poses certain challenges. In imaging such structures, it is sometimes desirable to image the side walls of the structure and to measure the radius of the tip of the structure in a non-destructive manner. Desired image resolutions can be on the order of 1 nm in the vertical direction (i.e. a direction which is normal to a measurement surface) and 10 nm in the lateral direction (i.e. a direction which is parallel to the measurement surface). Some profilometry methods are unable to provide such resolutions and thus such imaging criteria prevent the use of certain types of profilometry methods.
In one type of conventional stylus profilometer, a stylus having a sharp tip and coupled to a hinged arm is mechanically dragged along the sample surface. The deflection of the hinged stylus arm is measured and recorded as the surface profile. The use of a hinged stylus arm allows measurement of very rough surfaces, for example those with peak-to-peak heights greater than 1 mm. Probe-to-surface contact forces range from 10xe2x88x923 N to 10xe2x88x926 N. However, since the hinged stylus arm is partially supported by the stylus itself, physical rigidity limits the minimum stylus tip radius and hence the lateral resolution to about 0.1 mm.
In optical profilometry, many different optical phenomena (such as interference and internal reflection) can be utilized. The most popular technique is based on phase-measuring interferometry, in which a light beam reflecting off the sample surface is interfered with a phase-varied reference beam. The surface profile is deduced from the resulting fringe patterns. With a collimated light beam and a large photodetector array, the entire surface can be profiled simultaneously. This and other conventional optical profilometry methods are limited in lateral resolution by the minimum focussing spot size of about 0.5 xcexcm (for visible light). In addition, measurement values are dependent upon the surface reflectivity of the material being profiled.
In the current state of the art, only scanning probe microscopes can meet a 10 nm lateral resolution requirement. In these microscopes, an atomically sharp (or nearly so) tip at a very close spacing to the sample surface is moved over the surface using a piezoactuator. One type of scanning probe microscope is the atomic force microscope (AFM), which measures the topography of a surface with a probe that has a very sharp tip. A probe assembly includes a cantilever beam from which the probe, or microstylus extends. The probe terminates at the probe tip having a typical tip radius of less than 0.1 xcexcm. The probe typically has a length on the order of a couple of micrometers and the cantilever beam typically has a length between 100 xcexcm and 200 xcexcm.
In a contact mode atomic force microscope, the probe is moved relative to the surface of a sample and deflection of the cantilever is measured to provide a measure of the surface topography. More particularly, a laser beam is directed toward, and reflects off the back surface of the cantilever to impinge upon a sensor, such as a photodetector array. The electrical output signals of the photodetector array provide a topographical image of the sample surface and, further, provide feedback signals to a fine motion actuator, sometimes provided in the form of a piezoelectric actuator. In a constant force contact AFM, the fine motion actuator is responsive to the feedback signals for maintaining a substantially constant force between the probe tip and the sample, such as forces on the order of 10xe2x88x928 N to 10xe2x88x9211 N.
Contact atomic force microscopy offers high lateral and vertical resolutions, such as less than 1 nm vertical resolution and less than 50 nm lateral resolution. Further, since the contact AFM relies on contact forces rather than on magnetic or electric surface effects, advantageously the contact AFM can be used to profile conductive and non-conductive samples. However, the maximum surface roughness that can be profiled is much less than that of conventional stylus profilometers which use a linear variable differential transducer (LVDT).
In the non-contact atomic force microscope, long range van der Waals forces are measured by vibrating the cantilever near its resonance frequency and detecting the change in the vibrational amplitude of a laser beam reflected off the cantilever due to a change in the force gradient caused by changes in the surface profile. The non-contact atomic force microscope offers non-invasive profiling. However, the technique has some disadvantages when compared to contact atomic force microscopy. First, van der Waals forces are hard-to-measure weak forces, rendering the microscope more susceptible to noise. Secondly, the probe tip must be maintained at a fixed height above the sample, typically on the order of a few nanometers, and the feedback control necessary to maintain this spacing must operate slowly to avoid crashing the probe tip on the sample. Thirdly, since the tip is always floating above the surface, the effective tip radius is increased and hence the achievable lateral resolution is decreased.
AFM was primarily developed for high-resolution 3-D imaging (profilometry) of atomically flat samples. In that case, the probe tip is scanned over the sample and only the apical region of the probe interacts with the profiled surface. Therefore, AFM images will closely reproduce the topography regardless of distortions in the probe away from the apex. Accordingly, when stylus instruments are used in profilometry, the implicit assumption is that only the very apex of the stylus touches the surface at all points.
However, when structures having relatively high aspect ratio features are imaged, the AFM and stylus images can be quite different from the real topography. That is also the case when the dimensions of the sample are comparable to those of the employed probe (AFM probe or stylus). The reason for this deviation is that areas of the probe other than the apex (for instance, the probe sides) interact with the sample as well. The image distortion caused by the interaction of the probe with the surface is typically referred to as image convolution. These two conditions for significant convolution distortionxe2x80x94reduced sample dimensions and high aspect ratio occur frequently.
In many engineering fields, the characteristic dimensions of the samples or the features of interest lie well within the micrometer and sub-micrometer ranges. These fields include but are not limited to nanotechnology, micro-electromechanical systems (MEMS), semiconductor devices and storage media, micro-sensors, and blade fabrication. The investigated features could be photo-resist trenches in silicon wafers, memory pillars in quantum magnetic media devices, roughness in smooth optical surfaces, the radius of curvature of field emission probes and parts of micro-machines. Thus, images of such structures can be distorted by convolution errors.
The level of convolution is greatly dependent on the relative size and shape of the employed probe with respect to the sample. Different probes can interact with the sample generating different distorted images. Convolution seriously reduces metrology accuracy. The deviations in the measurement of radius of curvature of high aspect ratio samples is proportional to the radius of the probe. Therefore, samples with dimensions similar to those of the probe will generate images with close to a 100% radius measurement error. Width measurements taken from images of photo-resist trenches are embedded with deviations proportional to the square of the height of the probe (for nearly parabolic probes). Probe geometry and size can also affect texture parameter (e.g. roughness) measurements due to convolution.
In order to achieve high metrology accuracy in micrometer and sub-micrometer measurements, convolution effects must be minimized or eliminated from stylus and AFM images. Techniques that correct such effects are known as deconvolution methods. Deconvolution is necessary in applications in which the sample feature dimensions are in the same range as the size of the probe tip, therefore resulting in strong image convolution. Prior art deconvolution techniques include scanning a xe2x80x9cstandard samplexe2x80x9d (i.e. a sample having a known surface shape) with a probe to provide a mean curve for the probe shape, an inner curve for the probe shape, and an outer curve for the probe shape, thereby characterising the probe shape. One problem with this approach, however, is that errors in the initial probe calibration propagate to all other measurements. Another problem with this approach is that the shape of the probe change and to problems over time because of physical changes in probe due to probe wear.
It is, therefore, desirable to provide a deconvolution technique that does not rely on probe characterization. It is also desirable to provide a deconvolution technique which is not degraded by probe wear.
In view of the above problems and limitations of existing AFM probe calibration and deconvolution techniques, the existence of convolution errors when measuring high aspect ratio features and when sample feature dimensions are in the same range as the size of the probe tip, and in accordance with the present invention, it has been recognized that multiple images can be used to reduce convolution errors in the measured image of a sample without the need for probe characterization. It would therefore be desirable to provide an apparatus and method to deconvolve a sample image using multiple measured images without having to accurately characterize the measuring probe or to recalibrate the probe as it wears.
In accordance with the present invention, an apparatus utilizing contact atomic force microscopy (AFM) includes a probe, a controller operative to move the probe into a first vantage point relative to the sample to produce a first image, and to move the probe into a second vantage point relative to the sample to produce a second image. The apparatus further includes a deconvolution processor which deconvolves the first image and the second image to produce an image of the sample. With such an arrangement, a sample can be measured by obtaining and processing multiple images without utilizing probe characterization or correcting for probe wear. The apparatus thus utilizes multiple images at different vantage points to remove the convolution errors caused by the probe and sample shape. Furthermore, since the apparatus does not require a conventional probe characterization process, changes in the shape of the probe due to wear from use or from other causes do not effect the accuracy of the convolution.
In accordance with a further aspect of the invention, a deconvolution method includes moving a probe in a first scanning pattern to generate a first image of the sample, changing said probe""s vantage point, moving the probe in a second scanning pattern to generate a second image of the feature, and deconvolving the image of the sample using the first image and the second image. With this particular technique, a process for deconvolving an image without utilizing probe characterization is provided. The process is also unaffected by changes in probe shape due to wear or other causes. This technique is thus advantageous when using a microscope to measure relatively high aspect ratio samples. Furthermore, since the microscope images the sample at different angles, problems which arise due to regions where there is no contact between the sample and probe tip (e.g. so-called shadow zones) are reduced.
In a first embodiment, the deconvolution technique utilizes an iterative process. After generating multiple images of a sample from different vantage points, the process begins by generating two or more estimates of the probe shape using a first image. The estimates can be generated using a blind deconvolution method. Next using an erosion technique, each of the estimates of the probe shapes is used to obtain a corresponding estimate of the sample shape. Thus if two estimates of the probe shape are generated, then two estimates of the sample shape are obtained. At least two estimates of the probe shape are then combined to provide a new probe estimate. Similarly, at least two estimates of the sample shape are combined to provide a new sample shape estimate. The process of combining sample estimates (including newly computed sample estimates) to generate more sample estimates can be repeated any desired number of times. Similarly, the new sample shape estimates can be utilized to generate new probe shape estimates. The process of generating new probe shape estimates can also be repeated any desired number of times. In one embodiment, the above iterative process can be repeated until the changes in the newly computed sample shape and probe shape estimates are below a predetermined threshold when compared with the estimates from previous iteration. With such an arrangement an accurate estimate to the sample shape is obtained without the need for probe characterization. If additional images used, the fidelity of the estimated sample is increased.
In another embodiment, the deconvolution technique utilizes Legendre transforms in the processing of images to produce sample and probe measurements. After generating two images of a sample from different vantage points, the Legendre transform of the first and second image are obtained. These transforms are used in a system of equations that relate the transform of the sample with a first transform of the probe and the transform of the first image, the transform of the sample with a transform of the probe from the changed vantage point and the transform of the second image and relating the first transform of the probe, the transform of the probe from the changed vantage point and the angle between the first and second vantage point. After obtaining a Legendre transform of the first image and obtaining a Legendre transform of the second image, a parametric function is provided to describe the probe geometry and then by establishing how the upright and the rotated versions are geometrically related.
The parametric function provides a functional dependency between the probe transform in the first orientation and the probe transform from the second vantage point which allows a Legendre transform of the probe to be eliminated from the system of equations. Solving the system of equations by a least squares algorithm provides a Legendre transform of the sample. Finally, the sample is recovered from the Legendre transform of the sample. The probe geometry can also be recovered from the solution for the sample shape. With such an arrangement a partial but exact reconstruction of the sample shape is obtained without the need for probe characterization.